The author states they were banned for linking to their article [1] challenging Flat Earther's to take the "flat Earth route" from Johannes Burg to Sydney and beat the commercial great-circle flight. But what exactly would the "flat Earth" route be? Do they have a consistent claim about what the layout of the Earth is? It should depend on the Flat Earth model someone is using. (Though I suspect they'd all agree that…
In an unrestricted case, you can always select a map where that any real geodesic is a line in your flat map. I guess to prove that the surface is not flat, you need to measure the more distances, like measuring the four sides of a quadrilateral and then the two diagonal. (I think it is not possible using geodesics, without measuring one distance or an angle or a surface.)
The nice part of Gaussian curvature is that you can measure it in the surface, without a model of the 3D word that is "around" it. https://en.wikipedia.org/wiki/Gaussian_curvature